The Long and Winding Road
The elegant curve is one of the most reliable ways to add interest and depth to a landscape composition. When we see an "S" shape in our line of view it is usually in the form of a winding road, or a garden path or a trail through the woods. When we see the edges of the curve, they lead us forward into the body of the picture.
Roads, paths, rivers, streams, and trails invite us to follow them. They are places people go.
Straight ahead? (yawn)
It may be the quickest route between two points, but a straight ribbon of highway is not very interesting. It is static and does not invite the viewer into the whole composition. Your eyes go right where the orthogonal rays of the road pull you. A point of no interest. Very direct but not inticing.
It can be done this way of course. You have to slow down the trip down the street with elements impeding your eyes urge. Or you can orchestrate a huge payoff at the end of that road, like a cowboy riding off into a blazing sunset.
A Sunday drive
The sinuous swirling "S" shape pulls you along its length in an undulating fashion. A path worn or freshly paved invites at least a visual walk, a peek up the way a bit.
A winding road takes you on a sightseeing tour of the rest of the composition, inviting you enjoy the interplay of shapes and elements found in the movement of the composition.
The Path
Here is an example of a path leading you into a painting. I often like to use a partial S "up around the bend" compositional tool like I did in this watercolor.
The path materializes from the heavy shadows of the trees. It leads you into the painting and wraps you around the edge of the path where you find the glowing foliage beyond, further up the path.